Question

A local arcade charges $15.00 for unlimited play time for the first hour, then $5.00 per additional hour. On a
piece of paper, write an equation that represents the cost to play, C, based on the number of hours played,
h. Then use the equation to calculate how much it would cost to play for three hours. Enter your answer for
C, including cents.

Answer 1

To represent the cost to play, \( C \), based on the number of hours played, \( h \), we can set up the equation as follows:

\[
C = \begin{cases}
15 & \text{if } 0 < h \leq 1 \\
15 + 5(h - 1) & \text{if } h > 1
\end{cases}
\]

This means:
- For the first hour (0 to 1 hour), the cost \( C \) is $15.00.
- For any hours beyond the first hour, the cost will be $15.00 plus $5.00 for each additional hour.

Now, let's calculate the cost for 3 hours:

Since \( h = 3 \) which is greater than 1, we will use the second part of the equation:

\[
C = 15 + 5(h - 1)
\]

Substituting \( h = 3 \):

\[
C = 15 + 5(3 - 1)
\]
\[
C = 15 + 5(2)
\]
\[
C = 15 + 10
\]
\[
C = 25
\]

Thus, \( C \) for 3 hours is \(\$25.00\).